Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 30: Problem 23

A charged pion can decay either into a muon or an electron. The two decay modes of a \(\pi^{-}\) are: \(\pi^{-} \rightarrow \mu^{-}+\bar{v}_{\mu}\) and \(\pi^{-} \rightarrow \mathrm{e}^{-}+\bar{v}_{\mathrm{e}} .\) Write the two decay modes for the \(\pi^{+}\) [Hint: \(\pi^{+}\) is the antiparticle of $\pi^{-} .$ Replace each particle in the decay reaction with its corresponding antiparticle.]

Short Answer

Expert verified
Answer: The decay modes of a \(\pi^{+}\) are: 1. \(\pi^{+} \rightarrow \mu^{+}+v_{\mu}\) 2. \(\pi^{+} \rightarrow \mathrm{e}^{+}+v_{\mathrm{e}}\)

Step by step solution

01

Determine the antiparticles in the first decay mode

To find the decay mode of the \(\pi^{+}\), we first consider the first decay mode of the \(\pi^{-}\) and replace each particle with its corresponding antiparticle: - \(\pi^{-} \rightarrow\) antiparticle: \(\pi^{+}\) - \(\mu^{-} \rightarrow\) antiparticle: \(\mu^{+}\) - \(\bar{v}_{\mu} \rightarrow\) antiparticle: \(v_{\mu}\)
02

Write decay mode 1 for \(\pi^{+}\)

Using the antiparticles determined in Step 1, we rewrite the first decay mode of the \(\pi^{-}\) for the \(\pi^{+}\): \(\pi^{+} \rightarrow \mu^{+}+v_{\mu}\)
03

Determine the antiparticles in the second decay mode

Next, we consider the second decay mode of the \(\pi^{-}\) and replace each particle with its corresponding antiparticle: - \(\pi^{-} \rightarrow\) antiparticle: \(\pi^{+}\) - \(\mathrm{e}^{-} \rightarrow\) antiparticle: \(\mathrm{e}^{+}\) - \(\bar{v}_{\mathrm{e}} \rightarrow\) antiparticle: \(v_{\mathrm{e}}\)
04

Write decay mode 2 for \(\pi^{+}\)

Using the antiparticles determined in Step 3, we rewrite the second decay mode of the \(\pi^{-}\) for the \(\pi^{+}\): \(\pi^{+} \rightarrow \mathrm{e}^{+}+v_{\mathrm{e}}\) The two decay modes for the \(\pi^{+}\) are: 1. \(\pi^{+} \rightarrow \mu^{+}+v_{\mu}\) 2. \(\pi^{+} \rightarrow \mathrm{e}^{+}+v_{\mathrm{e}}\)

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

What is the de Broglie wavelength of a proton with kinetic energy $1.0 \mathrm{TeV} ?$
Three types of sigma baryons can be created in accelerator collisions. Their quark contents are given by uus, uds, and dds, respectively. What are the electric charges of each of these sigma particles, respectively?
When a proton and an antiproton annihilate, the annihilation products are usually pions. (a) Suppose three pions are produced. What combination(s) of \(\pi^{+}, \pi^{-},\) and \(\pi^{0}\) are possible? (b) Suppose five pions are produced. What combination(s) of \(\pi^{+}, \pi^{-},\) and \(\pi^{0}\) are possible? (c) What is the maximum number of pions that could be produced if the kinetic energies of the proton and antiproton are negligibly small? The mass of a charged pion is \(0.140 \mathrm{GeV} / c^{2}\) and the mass of a neutral pion is \(0.135 \mathrm{GeV} / c^{2}.\)
Which fundamental force is responsible for each of the decays shown here? [Hint: In each case, one of the decay products reveals the interaction force.] (a) \(\pi^{+} \rightarrow\) \(\mu^{+}+v_{\mu},\) (b) $\pi^{0} \rightarrow \gamma+\gamma(\mathrm{c}) \mathrm{n} \rightarrow \mathrm{p}^{+}+\mathrm{e}^{-}+\bar{v}_{\mathrm{e}}$
A neutral pion (mass \(0.135 \mathrm{GeV} / \mathrm{c}^{2}\) ) decays via the electromagnetic interaction into two photons: $\pi^{0} \rightarrow \gamma+\gamma$ What is the energy of each photon, assuming the pion was at rest?
See all solutions

Recommended explanations on Physics Textbooks

Rotational Dynamics

Read Explanation

Solid State Physics

Read Explanation

Mechanics and Materials

Read Explanation

Particle Model of Matter

Read Explanation

Conservation of Energy and Momentum

Read Explanation

Fundamentals of Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free